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March 27, 2017

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x,y and z are positive integers such that x<y,x+y=201,z−x=200. What is the maximum value of x+y+z?

  • Inequality Sum - ,

    x + y = 201

    y = 201 - x

    y > x that's why x < 201 / 2

    x < 100.5

    Nearest integer:

    x = 100


    x + y = 201

    y = 201 - x

    y = 201 - 100

    y = 101


    z − x = 200

    z = 200 + x

    z = 200 + 100

    z = 300


    x + y + z = 100 + 101 + 300 = 501

  • Inequality Sum - ,

    OR

    x + y = 201

    y = 201 - x


    z − x = 200

    z = 200 + x


    x + y + z = x + 201 - x + 200 + x

    x + y + z = 401 + x


    x + y = 201

    mean :

    x < 201 / 2

    x < 100.5

    ________________________________________

    For example :

    If x = 101

    y = 201 - x = 201 - 101 = 100

    That not satisfie condition :

    x < y


    If x = 102

    y = 201 - x = 201 - 102 = 99

    That not satisfie condition :

    x < y


    If x = 103

    y = 201 - x = 201 - 103 = 98

    That not satisfie condition :

    x < y

    etc.

    ________________________________________

    That's why :

    x < 201 / 2

    x < 100.5

    Largest integer less of 100.5 are 100

    so

    x = 100


    x + y + z = 401 + x = 401 + 100 = 501

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